21). The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is

A). \( \Large 2520 m^{2} \)

B). \( \Large 2480 m^{2} \)

C). \( \Large 2420 m^{2} \)

D). None of the above

View Answer

Correct Answer: \( \Large 2520 m^{2} \)

Let the length of rectangle = L m

Breadth of rectangle = B m

using conditions from the question,

L - B = 23 ....(i)

2(L + B) = 206

L + B = 103 ....(ii)

On adding Eqs. (i) and (ii), we get

2L = 126

=> L = 63 m

=> B = 103-63=40m

Then, area of rectangle = \( \Large L\times B \)

= \( \Large 63\times 40 \)

= \( \Large 2520 m^{2} \)

22). If the length of a rectangle decreases by 5 m and breadth increases by 3 m, then its area reduces 9 sq m. If length and breadth of this rectangle increased by 3 m and 2 m respectively, then its area increased by 67 sq m. What is the length of rectangle?

A). 9 m

B). 15.6 m

C). 17 m

D). 18.5 m

View Answer

Correct Answer: 17 m

Let length and breadth of a rectangle is x and y. Then, as per first condition,

(x-5)(y+3)=xy-9

=> xy-5y+3x-15=xy-9

=> 3x-5y=6 .....(i)

As per second condition,

(x+3)(y+2)=xy+67

=> xy+3y+2x+6=xy+67

=> 2x + 3y = 61 .....(ii)

On multiplying Eq. (i) by 3 and Eq. (ii) by 5 then adding, we get

9x - 15y = 18
10x + 15y = 305
----------------
=> 19x = 323

=> x = \( \Large \frac{323}{19} \)=17

Hence, the length of rectangle is 17 m

23). The area of a rectangle whose length is 5 more than twice its width is 75 sq units. What is the perimeter of the rectangle?

A). 40 units

B). 30 units

C). 24 units

D). 20 units

View Answer

Correct Answer: 40 units

Let the width of the rectangle = x units

Length = (2 x + 5) units

According to the question,

Area = x(2x + 5)

=> 75 = \( \Large 2x^{2}+5x \)

=> \( \Large 2x^{2} +5x-75=0\)

=> \( \Large 2x^{2} +15x-10x-75=0\)

=> x(2x+15)-5(2x+15)=0

=> (2x+15)(x-5)=0

=> x = 5 and \( \Large \frac{-15}{2} \)

Width cannot be negative.

Width = 5 units

Length=2x+5 =\( \Large 2\times 5+5 \)=15 units

Perimeter of the rectangle

= 2(15 + 5) = 40 units

24). Area of a rectangular field is \( \Large \Large 3584 m^{2} \) and the length and the breadth are in the ratio 7 : 2, respectively. What is the perimeter of the rectangle?

25). The length and perimeter of a rectangle are in the ratio of 5:18. What will be the ratio of its length and breadth?

A). 4 : 3

B). 3 : 5

C). 5 : 4

D). 4 : 7

View Answer

Correct Answer: 5 : 4

According to the question,

\( \Large \frac{l}{2(l+b)}=\frac{5}{18} \)

=> 10 l+ 10 b=18 l => 8 l=10 b

=> \( \Large \frac{l}{b}=\frac{10}{8}=\frac{5}{4} \)

l : b = 5 : 4

Hence, ratio of length and breadth of a rectangle is 5 : 4.

26). A rectangle has 20 cm as its length and 200 sq cm as its area. If the area is increased by \( \Large \Large 1\frac{1}{5} \) times the original area by increasing its length only then the perimeter of the rectangle so formed (in cm) is

A). 72

B). 60

C). 64

D). 68

View Answer

Correct Answer: 68

\( \Large l_{1} \) = 20 cm, \( \Large A_{1} \) = 200 sq cm

\( \Large b_{1} \) = \( \Large \frac{200}{20} \) = 10 cm

Now,\( \Large A_{2} \) = \( \Large 200\times 6/5 \)= 240 sq cm

\( \Large b_{2} \) = 10 cm

\( \Large l_{2} \) = \( \Large \frac{240}{10} \) = 24 cm

Perimeter of new rectangle = 2(\( \Large l_{2}+b_{2} \))

= 2(24+10)= \( \Large 2\times 34 \)=68cm.

27). A ground \( \Large \Large 100\times 80 m^{2} \) has, two cross roads in its middle. The road parallel to the length is 5 m wide and the other road is 4 m wide, both roads are perpendicular to each other. The cost of laying the bricks at the rate of RS. 10 per \( \Large \Large m^{2} \) , on the roads, will be

28). The breadth of a rectangle is 25 m. The total cost of putting a grass bed on this field was RS. 12375, at the rate of RS. 15 per sq m. What is the length of the rectangular field?

A). 27 m

B). 30 m

C). 33 m

D). 32 m

View Answer

Correct Answer: 33 m

Area of the rectangular field

= \( \Large \frac{12375}{15} \)=825 sq m.

According to the question,

\( \Large L\times B \) = 825 [L = length and B = breadth]

=> \( \Large L\times 25 \) = 825

L = \( \Large \frac{825}{25} \)=33 m

29). The length and the breadth of a rectangular plot are in the ratio of 5:3. The owner Spends RS. 3000 for surrounding it from all the sides at the rate of RS. 7.5 per metre. What is the difference between the length and breadth of the plot?